How to Arrange Decimal Numbers in Ascending Order
To manually arrange decimals in order from least to greatest, below shows how I would sort the following sample set.
0.15, 2.63, 0.008, 5, 4.27, 1.83, 3.13, 3.05, 4.0192
Step #1: Place the decimals in a grid with the decimal points all lined up in the same column, and add zeros to decimals as needed so that all decimals have the same number of places (in this case, 4 places).
| Decimal Grid | |||||
|---|---|---|---|---|---|
| 0 | . | 1 | 5 | 0 | 0 |
| 2 | . | 6 | 3 | 0 | 0 |
| 0 | . | 0 | 0 | 8 | 0 |
| 5 | . | 0 | 0 | 0 | 0 |
| 4 | . | 2 | 7 | 0 | 0 |
| 1 | . | 8 | 3 | 0 | 0 |
| 3 | . | 1 | 3 | 0 | 0 |
| 3 | . | 0 | 5 | 0 | 0 |
| 4 | . | 0 | 1 | 9 | 2 |
Step #2: Convert each decimal to an integer by dropping the decimal point and any leading zeros, and then list each result in a new sort column. This is just a shortcut to multiplying each decimal by the denominator of the right-most decimal place (in this case, the 1/10000 place).
| Decimal Grid | Sort | ||||||
|---|---|---|---|---|---|---|---|
| 0 | . | 1 | 5 | 0 | 0 | => | 1500 |
| 2 | . | 6 | 3 | 0 | 0 | => | 26300 |
| 0 | . | 0 | 0 | 8 | 0 | => | 80 |
| 5 | . | 0 | 0 | 0 | 0 | => | 50000 |
| 4 | . | 2 | 7 | 0 | 0 | => | 42700 |
| 1 | . | 8 | 3 | 0 | 0 | => | 18300 |
| 3 | . | 1 | 3 | 0 | 0 | => | 31300 |
| 3 | . | 0 | 5 | 0 | 0 | => | 30500 |
| 4 | . | 0 | 1 | 9 | 2 | => | 40192 |
Step #3: Reorder the rows based on the sort column from least to greatest, like this:
| Decimal Grid | Sort | ||||||
|---|---|---|---|---|---|---|---|
| 0 | . | 0 | 0 | 8 | 0 | => | 80 |
| 0 | . | 1 | 5 | 0 | 0 | => | 1500 |
| 1 | . | 8 | 3 | 0 | 0 | => | 18300 |
| 2 | . | 6 | 3 | 0 | 0 | => | 26300 |
| 3 | . | 0 | 5 | 0 | 0 | => | 30500 |
| 3 | . | 1 | 3 | 0 | 0 | => | 31300 |
| 4 | . | 0 | 1 | 9 | 2 | => | 40192 |
| 4 | . | 2 | 7 | 0 | 0 | => | 42700 |
| 5 | . | 0 | 0 | 0 | 0 | => | 50000 |
If you ignore the added zeros in the table above, the orginal decimals listed in ascending order would be as follows:
| 1 | 0.008 |
| 2 | 0.15 |
| 3 | 1.83 |
| 4 | 2.63 |
| 5 | 3.05 |
| 6 | 3.13 |
| 7 | 4.0192 |
| 8 | 4.27 |
| 9 | 5 |
How to Arrange Decimal Numbers in Descending Order
To manually arrange decimals in order from greatest to least, perform the same steps to create the sort column as you did for ascending order, but this time reorder the rows based on the sort column from greatest to least.
| Decimal Grid | Sort | ||||||
|---|---|---|---|---|---|---|---|
| 5 | . | 0 | 0 | 0 | 0 | => | 50000 |
| 4 | . | 2 | 7 | 0 | 0 | => | 42700 |
| 4 | . | 0 | 1 | 9 | 2 | => | 40192 |
| 3 | . | 1 | 3 | 0 | 0 | => | 31300 |
| 3 | . | 0 | 5 | 0 | 0 | => | 30500 |
| 2 | . | 6 | 3 | 0 | 0 | => | 26300 |
| 1 | . | 8 | 3 | 0 | 0 | => | 18300 |
| 0 | . | 1 | 5 | 0 | 0 | => | 1500 |
| 0 | . | 0 | 0 | 8 | 0 | => | 80 |
If you ignore the added zeros in the table above, the orginal decimals listed in descending order would be as follows:
| 1 | 5 |
| 2 | 4.27 |
| 3 | 4.0192 |
| 4 | 3.13 |
| 5 | 3.05 |
| 6 | 2.63 |
| 7 | 1.83 |
| 8 | 0.15 |
| 9 | 0.008 |